Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
  • Is there the shortest notation defined for a vector obtained by projecting $\vec{A}$ onto $\vec{B}$?
  • Is there the shortest notation defined for the complementary vector of a vector obtained by projecting $\vec{A}$ onto $\vec{B}$?

Is it ok if I used $\vec{A}\parallel \vec{B}$ for the first case and $\vec{A}\perp\vec{B}$ for the last one?

share|improve this question
Shortest notation as in? –  Inceptio Mar 11 '13 at 8:46
@Inceptio: How do you usually denote each of those questions above? Can you make it shorter? –  cyanide-based food Mar 11 '13 at 8:48
I always just see $\operatorname{Proj}_{\vec{B}}(\vec{A})$. –  Alexander Gruber Mar 13 '13 at 22:54
@AlexanderGruber: and the complementary one? –  cyanide-based food Mar 13 '13 at 22:55
@GarbageCollector I don't know of a notation for that one. –  Alexander Gruber Mar 13 '13 at 22:57

2 Answers 2

up vote 3 down vote accepted

Actually, after thinking about it some more, I now remember seeing the following used in my abstract linear algebra class:

$$\operatorname{proj}_{\vec{B}}(\vec{A})$$ $$\operatorname{perp}_{\vec{B}}(\vec{A})$$

and these in my 2nd year physics curriculum:

$$\operatorname{Proj}_{\parallel}(\vec{B},\vec{A})$$ $$\operatorname{Proj}_{\perp}(\vec{B},\vec{A})$$

I am not sure if there is a standard notation for these. Personally, I like the first one, since the second does not make immediately clear what is being projected onto what.

I don't think that using $\vec{A}\parallel\vec{B}$ and $\vec{A}\perp \vec{B}$ because these are conventionally used as statements about $\vec{A}$ and $\vec{B}$, i.e. $\vec{A}\perp\vec{B}$ should be read "$\vec{A}$ is orthogonal to $\vec{B}$" rather than an expression which means "the component of $\vec{B}$ orthogonal to $\vec{A}$." I think if you wrote, for example, $$B\perp \operatorname{perp}_{\vec{B}}(\vec{A})$$ that any reader would recognize this as a true statement (perhaps a tautology).

If you're writing in a situation where you can define your own notation, and you really want something short, I might suggest $\vec{A}_{\vec{B}}^\parallel$ and $\vec{A}_{\vec{B}}^\perp$ or (my personal preference) $\mathbf{A}_{\mathbf{B}}^{\parallel}$ and $\mathbf{A}_{\mathbf{B}}^{\perp}$. $$\mathbf{A}=\mathbf{A}_{\mathbf{B}}^{\parallel}+\mathbf{A}_{\mathbf{B }}^{\perp}$$ just looks slick.

share|improve this answer
Agreed 100% except that I think your last notations should be e.g. $\bf{A}^\perp_\bf{B}$; it's the component of * A * normal to the axis defined by B, rather than vice versa (and I might go with $\bf{A}_{\perp\bf{B}}$, though that comes across a little more awkward). –  Steven Stadnicki Mar 14 '13 at 17:17
@StevenStadnicki Yes! You are right, that is much better. –  Alexander Gruber Mar 14 '13 at 19:08

It is a $pr_{\vec{B}}(\vec{A})$ for the first case. I think, there is no notation for the second.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.